Journal of Inequalities and Applications
Volume 2 (1998), Issue 3, Pages 235-253

On Ozeki’s inequality

Saichi Izumino,1 Hideo Mori,2 and Yuki Seo3

1Faculty of Education, Toyama University, Gofuku, Toyama 930, Japan
2Department of Mathematics, Osaka Kyoiku University, Kashiwara, Osaka 582, Japan
3Tennoji Branch, Senior Highschool, Osaka Kyoiku University, Tennoji, Osaka 543, Japan

Received 6 April 1997; Revised 30 June 1997

Copyright © 1998 Saichi Izumino et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We shall obtain the best bound in Ozeki’s inequality which estimates the difference of Cauchy’s inequality. We also give an operator version of Ozeki’s inequality which extends an inequality on the variance of an operator.